It is known per se to use anaerobic purification in the treatment of waste water originating from the agricultural industry or from the foodstuffs industry. This is because of the presence of dissolved organic constituents, such as for example constituents originating from the processing of potatoes, vegetables, cereals, etc. In the known method, undissolved constituents are separated from the waste water which is to be subjected to anaerobic purification at an earlier stage by means of settling or floatation. However, a problem is that one still has to deal with the solid waste separated in a prior step. This so-called solid waste has to be discharged separately. Solid waste of this type is, for example, processed to form animal fodder. However, not all solid waste of this type is suitable for processing to form, for example, animal fodder and the market for processing into further products, such as for example animal fodder, may also stagnate.